In a standard normal distribution, what z value corresponds to 17% of the data between the mean and the z value?

You're looking for a value such that



Because the distribution is symmetric, the value of in either case will be the same.

Now, because the distribution is continuous, you have that



The mean for the standard normal distribution is , and because the distribution is symmetric about its mean, it follows that .



You can consult a score table to find the corresponding score for this probability. It turns out to be .